Table Of ContentProbing Extra Dimensions with Neutrino Oscillations
P. A. N. Machadoa, H. Nunokawab and R. Zukanovich Funchala ∗
1
1
aInstituto de F´ısica, Universidade de S˜ao Paulo,
0
2 C. P. 66.318, 05315-970 S˜ao Paulo, Brazil
n bDepartamento de F´ısica, Pontif´ıcia Universidade Cat´olica do Rio de Janeiro,
a
C. P. 38071, 22452-970 Rio de Janeiro, Brazil
J
9
We consider a model where sterile neutrinos can propagate in a large compactified extra dimension (a) giving
] rise to Kaluza-Klein (KK) modes and the Standard Model left-handed neutrinos are confined to a 4-dimensional
h spacetimebrane. TheKKmodesmixwiththestandardneutrinosmodifyingtheiroscillationpattern. Weexamine
p
current experiments in this framework obtaining stringent limits on a.
-
p
e
h
[
1. Introduction toDiracmassesandmixingsamongactivespecies
1 and sterile KK modes. This can be derived from
v The introduction of singlet neutrino fields the action
(cid:90)
6 which can propagate in extra spatial dimen-
S = d4xdyıΨαΓ ∂JΨα
8 sions as well as in the usual three dimensional J
6 space may lead to naturally small Dirac neutrino (cid:90)
1 + d4xıν¯αγ ∂µνα
masses,duetoavolumesuppression. Ifthosesin- L µ L
.
1 glets mix with standard neutrinos they may have (cid:90)
10 an impact on neutrino oscillations, even if the + d4xλαβHν¯LαΨβR(x,0)+h.c.,
sizeofthelargestextradimensionissmallerthan
1
where Γ ,J = 0,..,4 are the 5-dimensional
: 2×10−4m(thecurrentlimitfromCavendish-type J
v Dirac matrices, that after dimensional reduction
experiments which test the Newton Law).
i and electroweak symmetry breaking gives rise to
X
the effective neutrino mass Lagrangian
ar 2. Theoretical Framework L = (cid:88)mD (cid:34)ν(0)ν(0)+√2 (cid:88)∞ ν(0)ν(N)(cid:35)
HereweconsiderthemodeldiscussedinRef.[1] eff αβ αL βR αL βR
where the 3 standard model (SM) left-handed α,β N=1
neutrinos νLα and the other SM fields, including + (cid:88) (cid:88)∞ N ν(N)ν(N)+h.c.,
the Higgs (H), are confined to propagate in a a αL αR
α N=1
4-dimensional spacetime, while 3 families of SM
wheretheGreekindicesα,β =e,µ,τ, thecap-
singlet fermions (Ψα) can propagate in a higher
ital Roman index N = 1,...,∞, mD is a Dirac
dimensionalspacetimewithatleasttwocompact- αβ
ified extra dimensions, one of these (y) compact- mass matrix, ν(0) , ν(N) and ν(N) are the linear
αR αR αL
ified on a circle of radius a, much larger than the combinations of the singlet fermions that couple
size of the others so that we can in practice use a to the SM neutrinos ν(0).
αL
5-dimensional treatment. Inthiscontextonecancomputetheactiveneu-
The singlet fermions have Yukawa couplings trino transition probabilities
λ withtheHiggsandtheSMneutrinosleading
αβ P(ν(0) →ν(0);L)=
∗CToanlckagSivpeenccahtiNulOlaW, O20tr1a0n,tNo,euIttarilny,oSOespctiellmatbieorn4W-1o1r,ks2h0o1p0., (cid:12)(cid:12)(cid:12)(cid:12)(cid:88) (cid:88)∞ UααiUβ∗kWβ i(j0N)∗Wk(j0N)exp(cid:32)iλ2(jEN)a22L(cid:33)(cid:12)(cid:12)(cid:12)(cid:12)2
E-mail: [email protected]
i,j,kN=0
1
2
where U and W are the mixing matrices for ac- LEDinVacuum
tive and KK modes, respectively. Here λ(N) is 1.0
j 735km
a dimensionless eigenvalue of the evolution equa- 0.8
tion [1] which depends on the j-th neutrino mass
(mj), hence on the mass hierarchy, L is the base- (cid:174)Ν(cid:76)Μ 0.6 Standard
linTeoanildlusEtriastethwehnaetuitsrienxopeecnteerdgyw.e plot in Fig. 1 (cid:72)ΝPΜ 0.4 LED: ma0(cid:61)(cid:61)0510(cid:45)7m
the survival probabilities for ν → ν and ν¯ → 0.2 Normalhierarchy
µ µ e
ν¯ as a function of E. We show the behavior for Invertedhierarchy
e 0.0
the normal and inverted mass hierarchy assum- 1 2 3 4 5
ingthelightestneutrinotobemassless(m =0). E(cid:72)GeV(cid:76)
0
The effect of this large extra dimension (LED)
1.0
depends on the product m a. We observe that
j 180km
in the ν →ν channel the effect of LED is basi- 0.8
µ µ
callythesamefornormal(NH)andinverted(IH)
hierarchies, since in this case all the amplitudes Ν(cid:76)e 0.6
(cid:174)
involved are rather large. On the other hand, for (cid:72)ΝPe 0.4
ν¯ →ν¯ theeffectissmallerforNHasinthiscase
e e
0.2
the dominant m a term is suppressed by θ .
j 13
0.0
2 3 4 5 6 7 8
3. Results
E(cid:72)MeV(cid:76)
As we can observe in Fig. 1 the main effect of Figure 1. In the top (bottom) panel we show the
LED is a shift in the oscillation maximum with survival probability for ν (ν¯ ) as a function of
µ e
a decrease in the survival probability due to os- the neutrino energy for L=735 km (180 km) for
cillations to KK modes. This makes experiments a = 0 (no LED, black curve) and a = 5×10−7
such as KamLAND and MINOS, which are cur- m for normal hierarchy (dashed blue curve) and
rentlythebestexperimentstomeasure∆m2 and inverted hierarchy (dotted red curve).
(cid:12)
|∆m2 |, respectively, also the best experiments
atm
to test for LED. generate neutrinos with m = 0.2 eV. We have
0
We have used the recent MINOS [2] and Kam- verified that the inclusion of LED in the fit of
LAND [3] results and reproduced their allowed the standard atmospheric oscillation parameters
regions for the standard oscillation parameters. doesnotmodifyverymuchtheregionintheplane
For this and the LED study we have modified sin22θ ×|∆m2 | allowed by MINOS data. In
23 atm
GLoBES[4]accordingtoourpreviousanalysisof fact the best fit point as well as the χ2 remain
min
these experiments in [5] and [6]. the same as in the case without LED.
In Fig. 2, we present the excluded region in KamLAND data provide, for hierarchical neu-
the plane m × a, by MINOS, KamLAND and trinos with m → 0, a competitive limit only for
0 0
their combined data at 90 and 99% CL (2 dof). IH, in this case one gets a < 8.5(9.8)×10−7 m
When finding these regions all standard oscilla- at 90 (99)% CL. For degenerate neutrinos with
tion parameters where considered free. To ac- m = 0.2 eV one also gets from KamLAND
0
count for our previous knowledge of their values a < 2.0(2.3)×10−7 m at 90 (99)% CL. The in-
[7],wehaveaddedGaussianpriorstotheχ2func- clusion of LED in the fit of the standard solar
tion. As expected the limits provided by MINOS oscillation parameters here enlarges the region
(ν →ν ) are basically the same for NH and IH. in the plane tan2θ × ∆m2 allowed by Kam-
µ µ 12 (cid:12)
From their data we obtain a < 7.3(9.7)×10−7 LAND data. The best fit point changes from
m in the hierarchical case for m → 0 and ∆m2 = 7.6×10−5 eV2 and tan2θ = 0.62 to
0 (cid:12) 12
a < 1.2(1.6)×10−7 m at 90 (99)% CL for de- ∆m2 =8.6×10−5 eV2 andtan2θ =0.42,how-
(cid:12) 12
3
4. Conclusions
100
MINOSΝ (cid:174)Ν
Μ Μ We have investigated the effect of LED in neu-
excluded trinooscillationdataderivinglimitsonthelargest
extra dimension a provided by the most recent
10(cid:45)1 data from MINOS and KamLAND experiments.
(cid:76)V For hierarchical neutrinos with m0 → 0, MINOS
e
(cid:72) and KamLAND constrain a < 6.8(9.5) × 10−7
m0
m for NH and a < 8.5(9.8) × 10−7 m at 90
10(cid:45)2
(99)% CL for IH. For degenerate neutrinos with
m = 0.2 eV their combined data constrain a <
0
2.1(2.3)×10−7 m at 90 (99)% CL.
10(cid:45)3 We can estimate that the future Double
KamLAND CHOOZexperimentwillbeabletoimprovethese
limits by a factor 2 for the IH and by a factor
excluded 1.5forthedegeneratecase. UnfortunatelyNOνA
and T2K cannot improve MINOS limits. See [8]
10(cid:45)1
for any detail.
(cid:76)V RZF and HN thank Profs. Fogli and Lisi for
e
(cid:72)
m0 thecordialinvitationtoparticipateofNOW2010.
10(cid:45)2 This work has been supported by FAPESP,
FAPERJ and CNPq Brazilian funding agencies.
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